Issue 59

T. Sang-To et alii, Frattura ed Integrità Strutturale, 59 (2022) 141-152; DOI: 10.3221/IGF-ESIS.59.11

represents p a - local search factor) to get better results of PSO at T 2 = 50×200 = 10000. In other word, T 1 is only a half of T 2 . So now we can conclude that the combination of ES with improvement PSO (IPSO) are effective, fast and high performing for getting the desirable result.

Function (Fi)

Range

Dimension (d)

Min Fi

n

   1 i F x 1

2

( )

[-100, 100]

30

0

i

     2 1 1 n n i i i F x 

x

[-10, 10]

30

0

i

2

  

   

n

i

    1 1 i j

 

F

x

[-100, 100]

30

0

j

3







  x i n

F

max ,1 i i

[-100, 100]

30

0

4





  1 n





2

   2 2 x )



F

 x x 1 i

100(

1

[-30, 30]

30

0

i

i

5



i

1

n

 i F x   6 1 (

2



0.5)

[-100, 100]

30

0

i

n

 i F ix rand    4 i 7 1

  0,1

[-1.28, 1.28]

30

0

n

    8 1 i

F

x

x

sin

[-500, 500]

30

-418.9829x5

i

i

n

 2 ( i

2

 10cos(2 ) 10) x 

 i F x  9 1



[-5.12, 5.12]

30

0

i

   

   

  

  

n

n

1 n

1 n





2

 

 20exp 0.2



 exp cos(2 ) 20 x  

F

x

e

[-32, 32]

30

0

i

i

10





i

i

1

1

        2 cos i i x i    x  n n

1



F

1

[600, 600]

30

0

11

4000

i

1

i

1

  

  



n

1













2

2

  

 

2





  y





F

y

y

y

10sin(

)

1 1 10sin (

)

1





i

i

n

12

1

1

n u x



i

1

n



[-50, 50]

30

0



 ( ,10,100, 4) ( i x



i

1

1)

i

  1

: where y

i

4

n







2

  

   1)

2

2

 0.1{sin (3 ) x







F

x

x

1 1 10sin (3





i

i

13

1



i

1

[-50, 50]

30

0

n







2

2

 1 [1 sin (2 )]} x

   x



( , 5,100, 4) u x

n

n

i



i

1

Table 2: Classical Benchmark Functions.

146